Determine the domain of the function h(x)=4x/(x(x^2-16)) a.) {x│x≠4} b.) {x│x≠±4} c.) {x│x≠±4,x≠0} d.) {x│x≠±16,x≠0}

C.) {x│x≠±4,x≠0}

Step-by-step explanation:

h(x)=4x/(x(x^2-16))

the Domain is limited by the denominator

the denominator cannot equal 0

x*(x^2-16 ) ≠ 0

x≠0  and x^2 -16≠0

            x^2≠ 16

            x≠ ±4

step-by-step :

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.